95 Journal of Hydrology (NZ) 45 (2): 95-110 2006 © New Zealand Hydrological Society (2006) Estimating mean flow of New Zealand rivers R. Woods 1 , J. Hendrikx 1 , R. Henderson 1 and A. Tait 2 National Institute of Water and Atmospheric Research 1 P.O. Box 8602, Christchurch, New Zealand. Corresponding author: j.hendrikx@niwa.co.nz 2 Private Bag 14-901, Wellington, New Zealand Abstract Four simple models of mean annual runoff throughout New Zealand were evaluated, predominantly based on precipitation information and estimated evapotranspiration. Model results were compared to measurements and synthesised measurements of catchment runoff. Three models subtract an estimate of annual actual evapotranspiration from a precipitation surface. The first model assumes that annual actual evapotranspiration is a constant throughout New Zealand. The second model estimates annual actual evapotranspiration using a simple empirical model, which depends only on annual precipitation and annual potential evapotranspiration. The third model estimates annual actual evapotranspiration according to the ratios of potential evapotranspiration with annual precipitation, and a single water balance parameter which is estimated by independent calibration. The fourth model applies a regional bias correction to the results of the third model. The models are assessed by making estimates of runoff at model cells throughout New Zealand, and then averaging the cell runoff over the catchment boundary upstream of each river flow recording site. The catchment estimates of runoff are then compared with measured and synthesised runoff for each catchment, which have been adjusted to a common time period, in this case 1960-2001. The third model, which uses the ratios of potential evapotranspiration and precipitation, is found to give the greatest correlation with measured river flow. In terms of area, 87% of the total tested catchment area had modelled runoff within ±25% of the measured runoff when using the third model. Regional bias correction (fourth model) further enhances this surface, which can then be used to estimate runoff for un-gauged catchments in New Zealand. Introduction An understanding of the water balance of New Zealand is essential for the continued efficient utilisation and planning of water resources on a national scale and for making water resource estimates for areas where no flow measurements are available. Previous work has recognised this need, with many estimates made for particular catchments (e.g., Scarf, 1972; Toebes, 1972b; Aitcheson- Earl et al ., 2006). However, only Toebes (1972a) and Woods and Henderson (2003) have attempted to estimate the water balance for all New Zealand. Since the work of Toebes (1972a), New Zealand has seen the rapid expansion of water level and flow monitoring sites on a number of rivers, lakes and estuaries (Walter, 2000; Keane, 2001). Despite this expansion in flow monitoring, there are still many streams and rivers where river flow is